The other option is to default everything to one scene. This way, if you give recovery, it only works to allow you the supplemental healing and, possibly, the immediate, minor consequence healing after the scene is done.
I can't really think of any other power that has an effect over multiple scenes.
What you could do, is have the Player, in advance, invest 1 refresh from their pool for each extra scene they want the power to last. Then you can have the 'healing over time' effect and uses up refresh that can't be spent on multiple PCs.
In any case, I wonder how useful this is anyways.
For example, we have 3 Submerged PCs. One Pure Mortal, One Wizard and one Djinn.
Each PC has 1 refresh left.
The Djinn has
+3 Catch Iron or maybe some religious catach
-2 Toughness,
-2 Recovery
-2 Speed
-1 Shared abilities*
-5 Shared points
(total refresh 9/10)
(*-1 instead of -2 for modular abilities since you can't use it on yourself)
He's got 6 refresh worth of power that he can't use! Yes, the Wizard gets toughness and wings for one scene and the Pure Mortal gets Recovery.
But the Djinn could be so much more powerful if he kept those modular abilities to himself. Or even ditched modular abiliites and upgraded his toughness, took some stunts etc...
My point is this: would anyone actually take this power?
It would make for some cool RP if you attached an aspect of addiction to it. Maybe the Djinn is even compelled to pressure the others into taking the powers. That's the only angle I see for this. Mechanically, I don't see it as being overpowered.
Then again, I'm not seeing all the possibilities either. But having one tough PC (the one gaining all the powers) and one super weak one(the one granting powers) doesn't seem worth it. Or even that fun.